The reach of high bit-rate optical transmission systems becomes limited by PMD. The amount of PMD (expressed in terms of differential group delay (DGD) for the first order PMD) and also the orientation (expressed in terms of the principal states of polarization) fluctuate statistically with environmental changes like temperature. Therefore, a compensating device needs to be adaptive. Several solutions have been presented. As a general design, a polarization controller followed by a PMD compensating element is used.
FIG. 1 shows such a PMD compensator. The PMD compensator shown in FIG. 1 comprises polarization controller 101, DGD element 102 (fixed or variable), signal quality monitor 103, control logic 104, and interface 105. The signal quality monitor 103 provides feedback to the control logic 104. The control logic 104 adjusts the polarization controller 101 through interface 105 such that the PMD compensating element 102 applies inverse PMD to the transmission system. The interface 105 provides a reset-free, endless control to the polarization controller 101. As a feedback signal, any one of the bit-error rate, filtered spectral components, and the degree of polarization (DOP) can be used.
In FIG. 2, the dependence of the signal distortion, expressed in terms of Q-penalty, on the DGD (DGD) of a transmission fiber is shown. The signal distortion increases with the DGD of a transmission system. The higher the DGD is, the higher the signal distortion is. Also shown is the DOP as a function of the DGD of the transmission fiber. The DOP decreases with the DGD of a transmission system composed of a transmission fiber and a PMD compensator. The DOP reaches a maximum as the DGD of the transmission fiber approaches zero. Therefore, in one embodiment of a PMD compensator, the DOP can be used to adaptively control the feedback parameters on the polarization controller 101. The general control procedure is to adjust the feedback parameters such that the DOP reaches a maximum. In order to identify and reach the optimum compensation, some kind of dithering is required for adaptation. The control logic 104 dithers the control parameters applied on the polarization controller 101 and the DGD element 102 and optimizes the signal quality as measured by the monitor 103.
This procedure is outlined in FIG. 3. Changes are applied to the control parameters and the system response is measured. Depending on whether the signal quality has improved or not, changes are further applied in the same direction or the opposite direction, respectively. Performing this procedure over and over again, the PMD compensator tracks the optimum compensation point. The control parameters applied on the polarization controller 101 are slightly changed (dithered) (step 301) and the response is measured by, for example, the DOP (step 302). Then, it is checked whether the DOP has become higher than the previous DOP (step 303). If the DOP has become higher, the control parameters are further changed in the same direction tracking changing PMD conditions of the transmission fiber (step 304). Otherwise, the control parameters are changed such that the polarization controller 101 is driven in the opposite direction (step 305). This procedure can be described also as a trial and error method. In step 301, the control parameters are slightly changed around the current state in order to test whether the optimum has drifted. The amount of change needs to be high enough to clearly identify the optimum control point from, in general, the noisy and resolution-limited control parameter. On the other hand, the amount of applied changes (dithering steps) must not exceed a level at which significant distortion is introduced. Consequently, the maximum amount of applicable changes for the dithering steps (step size) is determined by the tolerable distortion due to the dithering procedure.
A problem arises due to the fact that the amount of introduced distortion (required for testing the optimum control point in the trial and error method) depends not only on the amount of applied parameter changes but also on the angular distance between the input polarization and the eigenaxis of the polarization controller. This is further explained using a Poincaré-sphere shown in FIG. 4. A state of polarization is described by two variables (angles), the azimuth θ and the ellipticity ε on the Poincaré-sphere. Here, a polarization controller composed of one or multiple sections of birefringent elements with adjustable retardance but fixed eigenaxis (eigenstate) 401 is assumed. Such a birefringent element can transform an input polarization into output polarizations located on a circle around the eigenaxis 401 of the birefringent element. Thus, the transformed polarization always describes a circle when the control parameters are changed. The radius of this circle depends on the angular distance between the input polarization and the eigenaxis 401. For the same applied changes in the feedback parameters, the amount of introduced signal distortion depends also on the angular distance between the input polarization and the eigenaxis 401 of the polarization controller. Therefore, the amount of polarization transformation and also the amount of introduced distortion becomes higher with increasing angular distance between the input polarization and the eigenaxis 401 for the same applied change of the control parameter.
Dithering the feedback parameters of the polarization controller with fixed step sizes is either too slow to track changing PMD conditions (small step size) or does not provide optimum compensation performance (large step size). This is illustrated in FIG. 5. In the case of too small step sizes (dithering steps), as indicated by (a), the PMD compensator is operational only as long as the PMD conditions of the transmission fiber do not change too fast. If the PMD conditions change, the PMD compensator is required to track these changes by varying the feedback parameters. Due to the limited amount of applicable parameter changes, the PMD of the transmission fiber may change faster than the PMD compensator is able to track when a fast disturbance arises. Thus, for too small step sizes, the PMD compensator will loose tracking in the case the PMD condition of the transmission fiber changes fast. In the case of too big dithering steps, as indicated by (b), the PMD compensator introduces from time to time high amounts of signal distortion incases of high angular distances between the input polarization and the eigenaxis of the polarization controller. Thus, the PMD compensator will be able to follow fast changes but the introduced Q-penalty required for dithering control will exceed a tolerable threshold.
This problem is known in the art through patent documents 1 and 2. There, the polarization controller comprises one or multiple sections of birefringent elements each with a fixed eigenstate of polarization but adjustable retardance. The amount of polarization change introduced by changing the control parameter applied on a birefringent element depends on the relative angle between the input polarization and the eigenstate of the birefringent element. At an extreme condition, the input polarization points into the direction of the eigenstate of the birefringent element. Then, by whatever amount the applied control parameter is changed, no change in polarization is introduced. The greater the angle between the input polarization and the eigenstate of the birefringent element is, the greater is the amount of polarization change for a given change of the control parameter. This is illustrated by FIG. 4. The possible polarization changes are located on, for example, circles 402 and 403 around the eigenstate 401. Depending on the distance of the input polarization from the eigenstate 401, the same change in the control parameter causes either a smaller polarization change (state S1->state S2) or a larger polarization change (state S3->state S4). The amount by which the overall polarization mode dispersion, and therefore the quality of data transmission measured e.g. by means of bit-error rate (BER), of an optical transmission system comprising a transmission fiber and a PMD compensator changes depends on the amount of introduced polarization change. The maximum amount of applicable parameter change for each feedback loop is therefore determined by the case for which the input polarization is at a maximum distance from the eigenstate of a birefringent element of the polarization controller. Otherwise an unacceptable amount of signal distortion would be introduced by the PMD compensator. On the other hand, the limited amount of applicable parameter change leads to little or even no change of the systems (transmission fiber plus PMD compensator) polarization mode dispersion in cases the input polarization is close to the eigenstate of a birefringent element. Under such circumstances tracking varying PMD conditions of the transmission fiber is difficult or even impossible. A method to overcome this is known in the art through the patent documents 1 and 2. Therein, the distance between the eigenstate of a birefringent element of a polarization controller and the input polarization is evaluated to adaptively change the amount of parameter change. For small distances a high amount of parameter change is applied at each feedback loop, while at large distances a small amount of parameter change is applied at each feedback loop. As indicated by (c) in FIG. 5, adaptive step size control allows for fast tracking of changing PMD conditions as well as the Q-penalty threshold is never exceeded.
This method, however, relies on the determination of the eigenstate of a birefringent element. The eigenstate can be estimated from the curvature between at least three polarizations measured at successive feedback loops. For example, the polarization state changes from state S1 to state S2 as shown in FIG. 4. The amount of polarization change is limited because otherwise an unacceptable amount of signal distortion would be introduced. Furthermore, the accuracy of polarization state measurements is limited by noise and other degrading effects. This makes the estimation of the eigenstate unreliable and the practical implementation difficult. Furthermore, time consuming calculations are required for curvature estimation, calculation of the eigenstate, and the computation of the angular distance to the actual state of polarization.
Another problem is that simple dithering (trial and error) involves a large amount of testing steps for a direction which decreases the amount of compensation and time is needed for correction. A third, general, problem is that there is no simple relation between the required polarization change and the amount of control parameter change. Sometimes large changes for the polarization controller applied voltages are necessary even if the required change in terms of polarization transformation is small. Therefore, with a simple dithering-like algorithm, only quasi-static compensation is possible. Such a PMD compensator will fail immediately for fast fluctuations due to fiber touching, etc.
Patent documents 3, 4, and 5 also describe PMD compensation in an optical transmission system.    Patent document 1    publication of European patent application, No. EP 1 170 890    Patent document 2    publication of Japan patent application, No. 2002-082311    Patent document 3    published Japanese translation of PCT international publication for patent application (WO98/29972), No. 2000-507430    Patent document 4    publication of Japan patent application, No. 2001-044937    Patent document 5    publication of Japan patent application, No. 2001-230728